Define the following propositions: .p: you drive over 65 miles per hour q you get a speeding ticket translate the following english sentence into logical expressions using the definitions above (a) you drive over 65 miles per hour, but you do not get a speeding ticket. (b) if you do not drive over 65 miles per hour, then you will not get a speeding ticket (c) you get a speeding ticket, but you did not drive over 65 miles per hour.

a.p→¬q

b.¬p→¬q

c.q→¬p

Step-by-step explanation:

p:You drive over 65 miles per hour

¬p: You do not drive over 65 miles per hour

q:You get a speeding ticket

¬q:You do not get a speeding ticket

(a) You drive over 65 miles per hour, but you do not get a speeding ticket

the first sentence is p and because the consequence is the opposite of q then is no q

p→¬q

(b) If you do not drive over 65 miles per hour, then you will not get a speeding ticket

The first sentence is the opposite of p (¬p), and the second sentence is the opposite of q

¬p→¬q

(c) You get a speeding ticket, but you did not drive over 65 miles per hour.

The first one is q, and the second one is the opposite of p so

q→¬p

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)